Aptekarev, Alexander I.Bogolubsky, Alexey I.Yattselev, Maxim L.2018-01-112018-01-112017Aptekarev, A. I., Bogolyubskii, A. I., & Yattselev, M. L. (2017). Convergence of ray sequences of Frobenius-Padé approximants. Sbornik: Mathematics, 208(3), 313. https://doi.org/10.1070/SM8632https://hdl.handle.net/1805/14999Let $\widehat\sigma$ be a Cauchy transform of a possibly complex-valued Borel measure $\sigma$ and $\{p_n\}$ a system of orthonormal polynomials with respect to a measure $\mu$, where $\operatorname{supp}(\mu)\cap\operatorname{supp}(\sigma)=\varnothing$. An $(m,n)$th Frobenius-Padé approximant to $\widehat\sigma$ is a rational function $P/Q$, ${\deg(P)\leq m}$, $\deg(Q)\leq n$, such that the first $m+n+1$ Fourier coefficients of the remainder function $Q\widehat\sigma-P$ vanish when the form is developed into a series with respect to the polynomials $p_n$. We investigate the convergence of the Frobenius-Padé approximants to $\widehat\sigma$ along ray sequences ${n/(n+m+1)\to c>0}$, $n-1\leq m$, when $\mu$ and $\sigma$ are supported on intervals of the real line and their Radon-Nikodym derivatives with respect to the arcsine distribution of the corresponding interval are holomorphic functions.enPublisher Policyconvergenceray sequencesFrobenius-Padé approximantsArticle